1、Value of 30-Year Mortgage 5-Years Out (6%)02,000,0004,000,0006,000,0008,000,00010,000,00012,000,00014,000,00016,000,0001%3%5%7%9%11%Market Interest RateMarket Value of MortgageCash from Mortgages and Cash Needed for CDs0200,000400,000600,000800,0001,000,0001,200,0001%2%3%4%5%6%7%8%9%10% 11% 12%Curre

2、nt Interest RateCash Flows From Mortgages and to CDsHedging v. Insuring05000010000015000020000025000030000035000040000045000000.511.522.533.54Price of WheatRevenue from WheatHedgedInsuredHedging with a Put-200002000400060008000100001200014000160005060708090100110120130140150Share PriceShare HoldingV

3、alue PutsFV PremiumTotal WealthState of the World ProbabilityPayoffMeanDeviationDev SQR- * ProbOne Failure0.50200000-2000004E+102E+10One Success0.54000002000002000004E+102E+10Sum =4E+10Sqrt |200000State of the World ProbabilityPayoffMeanDeviationDev SQR- * ProbOne Failure0.250200000-2000004E+101E+10

4、One Success0.5200000200000000Two Successes0.254000002000002000004E+101E+10Sum =2E+10Sqrt |141421.3562 , 121212222212122wwwwpStandard Deviations of Portfolios, rho = 0.2, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation Standard Deviations of

5、 Portfolios, rho = 0.8, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation Standard Deviations of Portfolios, rho = 0.5, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation Standard Devia

6、tions of Portfolios, rho = 0.2, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation Standard Deviations of Portfolios, rho = 0.0, sig = 0.2 0.000.020.040.060.0005101520253035404550Portfolio Size Standare Deviation Standard Deviations of Portfolios, rho = 1/(1-50) = -0.0204, sig = 0.2